Besides the canonical example of the AdS-Schwarzschild metric, there are various instances of extra-dimensional theories which would be good candidates for a holographic superconductor. In particular, the correct pole structure in Eq. (REF ) is found on the Hirn-Sanz metrics [1]}, [2]}, which were employed to develop duals for QCD and for new physics at the Electroweak scale, the AdS-dilaton metric [3]}, a specific type of metric designed to reproduce the Regge trajectories, and the Sakai-Sugimoto metric [4]}, [5]}, inspired by Witten's string theory model of D8 branes [6]}. Specific forms of the function \(h(z)\)  for these proposals are summarised below:
\(h(z) &=& \frac{p_2 (z)}{z^2} \textrm { (AdS-Schwarzschild~\cite {Witten:1998qj})} \nonumber \\&=& \frac{p_2 (z)}{z^2} \, e^{c_d (z/r_H)^{2 d}} \textrm { (Hirn-Sanz~\cite {Hirn:2005vk,Hirn:2006wg})}\nonumber \\&=& \frac{p_2 (z)}{z^2}\, e^{-z^2}\textrm { (AdS-dilaton~\cite {Karch:2006pv})} \nonumber \\&=& \frac{p_{11} (z)}{z^6} \textrm { (Sakai-Sugimoto~\cite {Evans:2008tv})}\nonumber \\\) 
